Enhanced macroscopic model for simulating dynamic behavior of elastomeric bearings including axial shortening effects

Elastomeric bearings undergo axial shortening as horizontal displacement increases. Existing studies predominantly focus on the static mechanical characteristics of bearings induced by axial shortening, while investigations concerning axial-shortening-effects on dynamic bearing responses remain insufficient. Two key limitations exist in current research: conventional macroscopic models cannot capture axial shortening behaviors of bearings under dynamic loading, and few studies distinguish the individual-bearing axial shortening responses from the vertical coupling interactions among multiple bearings within an isolation system. To address these gaps, this study incorporates a displacement-dependent variable stiffness function into the vertical spring of a baseline macroscopic model, developing an enhanced macroscopic model that enables the simulation of dynamic axial-shortening-effects on elastomeric bearings. The accuracy and robustness of the proposed model are validated against dynamic test data under extreme horizontal excitations. Comprehensive parametric analyses are further conducted based on the validated model. The main conclusions are drawn as follows: (1) Differential axial shortening among bearings generates vertical coupling interactions within the isolation system, leading to distinct dynamic mechanical behaviors of bearings compared with their quasi-static performance; (2) Axial shortening triggers vertical excitation of bearings, resulting in evident fluctuations in axial load and hysteretic responses; (3) Such axial-shortening-induced vertical excitation can be effectively mitigated by increasing the vertical stiffness and damping of elastomeric bearings.